A middle school math teacher wants students to learn how to calculate the area of a​ triangle, which involves multiplying the​ triangle's base​ (i. e., bottom​ side) by its height​ (measured by a line going perpendicular from the base to the opposite​ angle) and then dividing by 2. The formula A​ = ½ ​(b×h​) is the mathematical equivalent. What strategies might the teacher use to help students understand and remember this​ procedure?

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

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